Final answer:
To find the derivative f'(1) for the function f(x) = 7x - 3 + lnx, we differentiate each term to get 7 + 1/x and then evaluate it at x = 1 to find that f'(1) equals 8.
Step-by-step explanation:
If we are to find f'(1) for a given function f(x) = 7x - 3 + lnx, we need to use calculus to find the derivative of the function and then evaluate it at x = 1. The process of finding the derivative is known as differentiation. We must apply the rules of differentiation separately to each term of the function.
The term 7x differentiates to 7, because the derivative of x with respect to x is 1, and thus the coefficient remains unchanged. The constant term -3 differentiates to 0 because the derivative of a constant is zero. Lastly, the ln(x) derivative is 1/x, since the derivative of the natural logarithm function, ln(x), is 1/x.
Putting this together, we find that the derivative f'(x) is 7 + 1/x. To find the value of f'(1), we substitute x = 1 which gives us f'(1) = 7 + 1/1 = 8. Therefore, f'(1) = 8.